Blender changes image colors when rendering
PNG is a terrible format. You should forget it even exists.

Blender does only what the operator instructs it to do. If the setting are to output on a certain color space, then that is the color space it will use. If the original source is in a different color space blender has no way to guess what that might be. 

Any image displayed in the wrong color space will always look wrong.

When doing visual effects you need to plan how to have all of your material be in the same color space. If one source is encoded using a different gamut than the other they never going mix nicely and any transformation will further distort the color on one or the other. Long story short: you can't mix apples and oranges. 

All compositing should be made using linear values in a common color space.

The ideal scenario would involve controlling all of the variables.

Ingest your footage in resolve, set the correct input transforms, color space and gamut (Vlog to 709). Then export the plates as linear scene referred values (de-Log it), convert it then to the correct color space you are going to be working on (most likely 709): set the project to be Color Managed and use 709 scene as output color spaces. Export then as EXRs to be used in Blender. Work your magic in blender, export the elements to be combined back to resolve as linear-scene referred EXRs. then composite in fusion (read the suggested link). 

Else you need to go a more complicated route, which is to create a definition of V-log in the Ocio config, supply the correct LUT and color matrix, so that the footage ingested is linearized correctly and with the correct 709 gamut in blender. Work then your amazing magic in blender and re-encode as V-log and save as Tiff files. Bring those files in resolve and integrate them into your project.